An increased load on the alternator WILL draw more power from the engine to drive the alternator. Any increased load on the engine will reduce your fuel mileage, so the answer to your question is YES… An increase in electrical load WILL decrease your fuel economy.

yes, the energy for running the electronics must come from somewhere, as per the law of conservation of energy. The energy from the fuel is turned into rotational energy in the alternator which is used to charge the battery. The electronics in the car use the energy from the battery to give you light energy, sound energy etc

it ’s more a matter of installing a higher capacity alternator

yes, the extra load on the alternator translates to added load on the engine…